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Alcoholism has become a global threat and has a serious health consequence in the society. In this paper, a deterministic alcohol model is formulated, analyzed and the basic properties established. The reproduction number R₀ of system is determined. The steady states examined and local stability is found to be both locally and globally stable. The endemic state exhibit three equilibra solutions. Furthermore, time dependent control is incorporated into the system in order to establish the best strategy in controlling the alcohol consumption and gonorrhea dynamics, using Pontryagin’s Maximum Principle. The numerical results depict that the best strategy to controlling gonorrhea is the application of the three controls at the same time.